research papers

946 http://dx.doi.org/10.1107/S1600577515007390 J. Synchrotron Rad. (2015). 22, 946–955

Received 28 January 2015

Accepted 14 April 2015

Edited by P. A. Pianetta, SLAC National

Accelerator Laboratory, USA

Keywords: beam position monitor; X-ray

diffraction; K-edge absorption; phase space.

A phase-space beam position monitor forsynchrotron radiation

Nazanin Samadi,a* Bassey Bassey,b Mercedes Martinson,b George Belev,c

Les Dallin,c Mark de Jongc and Dean Chapmand

aBiomedical Engineering, University of Saskatchewan, 107 Wiggins Road, Saskatoon, SK, Canada S7N 5E5, bPhysics and

Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, SK, Canada S7N 5E2, cCanadian Light

Source, 44 Innovation Boulevard, Saskatoon, SK, Canada S7N 2V3, and dAnatomy and Cell Biology, University of

Saskatchewan, 107 Wiggins Road, Saskatoon, SK, Canada S7N 5E5. *Correspondence e-mail: nazanin.samadi@usask.ca

The stability of the photon beam position on synchrotron beamlines is critical

for most if not all synchrotron radiation experiments. The position of the beam

at the experiment or optical element location is set by the position and angle of

the electron beam source as it traverses the magnetic field of the bend-magnet

or insertion device. Thus an ideal photon beam monitor would be able to

simultaneously measure the photon beam’s position and angle, and thus infer

the electron beam’s position in phase space. X-ray diffraction is commonly used

to prepare monochromatic beams on X-ray beamlines usually in the form of a

double-crystal monochromator. Diffraction couples the photon wavelength or

energy to the incident angle on the lattice planes within the crystal. The beam

from such a monochromator will contain a spread of energies due to the vertical

divergence of the photon beam from the source. This range of energies can

easily cover the absorption edge of a filter element such as iodine at 33.17 keV.

A vertical profile measurement of the photon beam footprint with and without

the filter can be used to determine the vertical centroid position and angle of the

photon beam. In the measurements described here an imaging detector is used

to measure these vertical profiles with an iodine filter that horizontally covers

part of the monochromatic beam. The goal was to investigate the use of a

combined monochromator, filter and detector as a phase-space beam position

monitor. The system was tested for sensitivity to position and angle under a

number of synchrotron operating conditions, such as normal operations and

special operating modes where the photon beam is intentionally altered in

position and angle at the source point. The results are comparable with other

methods of beam position measurement and indicate that such a system is

feasible in situations where part of the synchrotron beam can be used for the

phase-space measurement.

1. Introduction

The trajectory of a photon beam can be determined if both the

position and angle can be found at some point along the

propagation direction. From knowledge of this beam’s posi-

tion and angle or its position in phase space, it is possible to

transform back to the source and determine the source co-

ordinates in phase space if the optics in the intervening loca-

tions and their effects are known.

This paper describes a method to simultaneously measure

the photon beam position and angle at one location. The

system was developed at the Canadian Light Source (CLS) on

the Biomedical Imaging and Therapy (BMIT) bend-magnet

beamline 05B1-1 (BM).

The CLS is a third-generation synchrotron facility with

a low electron beam emittance ("x = 18 nm rad, "y =

0.10 nm rad). Beam instability, be it electron or photon beam,

ISSN 1600-5775

can be a concern especially to the third-generation facilities. It

has adverse effects on the required low electron beam emit-

tance, effective brilliance of the synchrotron radiation, and

experiments performed at the experimental stations (Brefeld,

1989; Haga et al., 2000; Galimberti & Borghes, 2004; Rehm,

2013). The causes of beam instability and the methods of

reduction have been widely studied (Hettel, 1989; Bocchetta,

1996; Farvacque, 1996; Hettel, 2002), and the drive to ensure

and maintain a steady beam has led to the development of

different types of beam monitors (Billing, 1988; Izumi et al.,

1989; Johnson & Oversluizen, 1989; van Silfhout, 1999; Alkire

et al., 2000; Kyele et al., 2005; Bunk et al., 2005; Bergonzo et al.,

2006; Ilinski et al., 2007; Tucoulou et al., 2008; Leban et al.,

2010; Revesz et al., 2011; Xiao et al., 2012; Muller et al., 2012;

Cheng et al., 2013).

Photon beam position and angle instabilities at experi-

mental stations are attributed to fluctuations of stored elec-

tron beam orbit and vibrational and thermal distortion of

beamline optical components. The usual target for stability in

the vertical plane is 10% of the beam size in position and angle

(Hettel, 1989). Most of the available photon beam monitors

are sensitive to the beam position only, and hence the name

photon beam-position monitor (PBPM). However, the

measured beam position is determined by both the source

position and angle. A single PBPM does not provide inde-

pendent information about the photon beam source position

and angle (Tucoulou et al., 2008; Kachatkou et al., 2013). The

photon beam angle also needs to be monitored to account for

the negative effects of beam angle instability (Tucoulou et al.,

2008; Hahn et al., 1998; Kyele et al., 2007; Morse et al., 2010).

The use of two-photon PBPMs is common when the position

and angle of a photon beam is to be measured (Tucoulou et al.,

2008; Muller et al., 2012; Cheng et al., 2013).

At the CLS, beam instabilities are monitored by two diag-

nostic beamlines: the Optical Synchrotron Radiation (OSR)

beamline and the X-ray Synchrotron Radiation (XSR)

beamline (Bergstrom & Vogt, 2006). Most beamlines at the

CLS have provision for some type of PBPMs, but few are

actually implemented or used. These monitors are of the type

that measure only the photon beam position at some location

in the beamline.

As with almost all synchrotron experiments, imaging is

affected by photon beam motion. One of the imaging methods

used at the BMIT beamline is K-edge subtraction using an

iodine contrast element with a beam prepared by a bent Laue

monochromator. Measurements made with this system during

a period of electron beam instability gave the idea that we can

measure the photon beam position and angle or from it infer

the electron beam’s position in phase space.

We present a method for measuring the position and angle

of a photon beam simultaneously, i.e. using a phase-space

beam position monitor (ps-BPM). The method relies on the

energy-dispersive properties of flat crystals and makes use of

the absorption edge of a filter in the photon beam path to

determine a specific energy or angle of the photon beam. This,

coupled with a measurement of the beam in the absence of the

filter, allows beam position and angle to be determined.

1.1. Synchrotron radiation

The single electron vertical photon emission distribution

is properly described by a modified Bessel function of the

second kind (Thompson et al., 2009); however, this distribu-

tion is well modelled as a Gaussian function. This vertical

angular distribution mostly falls within a 1/� range in the

X-ray regime where � is the electron beam energy divided by

the electron rest mass (� = 5675 for the CLS). The electron

beam size and vertical angle distribution can also be described

as a Gaussian function. Therefore, the bend-magnet

synchrotron beam has a vertical distribution that is nearly

Gaussian. A measured comparison with theory for the vertical

distribution of the beam on the CLS BMIT bend-magnet

beamline is shown in Fig. 1 at 33.17 keV. As measured some

distance from the source, the vertical angle or position motion

of the electron source will move this distribution vertically.

Because the measurement distance from the source can be

tens of metres, the angle affects are amplified. For example,

the profile measured in Fig. 1 is at 26 m from the electron

beam source. In this figure the blue line is the measured profile

from the image at the top of the figure. The red dashed line is a

Gaussian fit to that profile. The fact that the red dashed line is

difficult to see indicates how closely the Gaussian fit is to the

actual beam profile. The black dashed line is a calculated

profile from the modified Bessel function (Thompson et al.,

2009) for the actual conditions of the measurement [CLS bend

magnet (2.9 GeV and 1.354 T) at 26 m from the source with

100 mm pixels and 33.17 keV photon energy].

1.2. Double-crystal monochromator at an absorption edge

Diffraction of X-rays in crystals can be thought of as arising

from constructive interference from reflections at lattice

planes as described by Bragg’s law,

research papers

J. Synchrotron Rad. (2015). 22, 946–955 Nazanin Samadi et al. � Phase-space beam position monitor 947

Figure 1Nearly Gaussian vertical beam profile as measured on the CLS BMITbend-magnet beamline. The picture at the top is an image of the beam.The plot at the bottom shows the measured beam profile from that image(blue) and a Gaussian fit (red dash). The red dotted line identifies thecenter. The red text gives the least-squares Gaussian fitting parameters.The vertical scale is in pixel units (100 mm pixel size). The calculatedbeam profile is shown as the black dashed line.

� ¼ 2dhkl sin �; ð1Þ

where � is the wavelength of the diffracted beam, � is the angle

between the incident beam and lattice planes, and dhkl (called

the d-spacing) is the spacing between the (h,k,l) lattice planes.

For an X-ray synchrotron beamline, usually a pair of

parallel crystals is used, one to monochromatize the incident

beam and one to diffract that beam back parallel to the inci-

dent beam. With a coordinated motion of the two crystals, a

range of energies can be chosen while keeping the mono-

chromatic beam from the second crystal in the same location

which is very useful for much of the research being done.

Additionally, the near unit reflectivity of the perfect crystals

often used means there is little intensity loss from the pair.

This arrangement is commonly called a double-crystal

monochromator (DCM) (Golovchenko et al., 1981).

When a DCM is tuned to an energy, for example, the K-

edge energy of an element, some of the transmitted beam will

be above and some below the mean energy due to the

dispersion properties of the crystals. This range of energies

arises from the range of incident photon beam angles onto the

lattice planes of the crystal and/or the energy bandwidth of the

crystal and the reflection used. The range of energies due to

angular divergence onto the planes is easily calculated using

Bragg’s law based on the monochromator reflection used and

the angular size of the beam passing through the system. A

schematic of a DCM arrangement is shown in Fig. 2.

As an example, assume a vertical angle range for the CLS of

1/� = 176 mrad. At 33.17 keV, the absorption edge of iodine,

the Bragg angle is 5.586� for the silicon (2,2,0) reflection. We

can estimate the range of wavelengths using the derivative of

Bragg’s law with respect to angle,

d� ¼ 2dhkl cos � d�: ð2Þ

For the conditions stated, the wavelength spread is 6.73 �

10�5 nm centered at 0.03738 nm. The matching energy spread

is 59.7 eV. Fig. 3 is a graphical representation, a DuMond

diagram (DuMond, 1937), of Bragg’s law in the vicinity of the

iodine K-edge.

There is also an energy or wavelength spread due to the

finite reflectivity width of the dispersion curve. For diffraction,

the energy or wavelength bandwidth is a fixed quantity away

from absorption edges of the crystal. For silicon (2,2,0) the

bandwidth is 56.6� 10�6. Thus the intrinsic wavelength spread

is 2.12 � 10�6 nm and the intrinsic energy spread is 1.88 eV.

This wavelength and energy spread is also shown in Fig. 3. The

energy spread due to divergence is almost 32 times that of the

intrinsic energy spread.

Schematically, the effect of an iodine filter on the trans-

mitted beam of a DCM set at 33.17 keV is shown in Fig. 2(c).

Note that the spectral content of the beam vertically increases

in energy from the bottom of the beam to the top. When the

middle energy of the beam is placed at the iodine K-edge then

the top of the beam will be absorbed more than the bottom

creating an asymmetric beam profile shown on the right side

of the figure. A calculation of the beam shape including the

DuMond dispersion effects is shown in Fig. 4.

research papers

948 Nazanin Samadi et al. � Phase-space beam position monitor J. Synchrotron Rad. (2015). 22, 946–955

Figure 2Schematic of the system used at the BMIT bend-magnet beamline. (a)Plan view of the double-crystal monochromator (DCM), contrastmaterial and detector. (b) Elevation view of the non-contrast or beamside; (c) elevation view with contrast material whose K-edge is at thevertical middle beam prepared by the DCM. Example plots at theright show the profile for the unfiltered beam (b) and contrast filteredbeam (c).

Figure 3DuMond Diagram for Si (2,2,0) at 33.17 keV for 1/� vertical divergence.The energy and angular ranges are shown for both vertical divergenceand intrinsic widths. The relatively large vertical divergence results in anenergy range that easily covers the K-edge of iodine.

Figure 4Calculated flux through a 60 mg cm�2 iodine filter from a Si (2,2,0) DCMat 33.17 keV on a CLS bend-magnet beamline.

2. What happens when the beam moves?

2.1. Unfiltered side of the beam

When a photon beam moves at the source location the

monochromatic beam after the DCM is sensitive to the

motion. If the source point moves up then the beam measured

at the detector location will also move up by the same amount.

If the beam moves in vertical angle then the beam at the

detector position will move by the product of the angle times

the distance from the source to the detector. This effect is

shown schematically in Figs. 5(a)–5(d) in the ‘Beam’ column.

The combination of vertical beam motion and angle is

yd ¼ yþDy0; ð3Þ

where yd is the measured vertical beam position at the imaging

detector, y is the vertical position of the electron beam source,

y0 is the vertical angle of the electron beam source and D is the

distance from the source to the detector.

2.2. K-edge filtered side of the beam

The K-edge of an element is a fixed energy and can be used

to locate that energy in the photon beam; energies above the

edge will be heavily absorbed and energies below the edge will

not. If the source moves vertically the location of the K-edge

transition will move the same amount at the detector. This is

because the vertical energy distribution of the photon beam is

not altered by this motion. If instead the beam at the source

moves in vertical angle the location of the edge will not move.

In this case the vertical photon beam energy distribution is

changed by the DCM but the vertical location of the K-edge at

the detector will not move because the angle is set by the

monochromator. Therefore the location of the K-edge at the

detector is a direct measure of the location of the source

vertically. This effect is shown schematically in Figs. 5(a)–5(d)

in the ‘Edge’ column. The location of the K-edge measured at

the detector is then simply

yc ¼ y; ð4Þ

where yc is the measured vertical K-edge location and y is the

vertical position of the electron beam source. Changes in the

vertical source angle do not change the location of the K-edge

at the detector.

3. Determining the electron source vertical positionand angle

We are now in a situation to be able to independently deter-

mine the vertical electron beam position and angle by

measuring the beam location through a DCM without a filter

(beam side) and the edge location with a K-edge filter in place

(edge side); using equations (3) and (4),

y0 ¼yd � yc

D; y ¼ yc: ð5Þ

It should be noted that changing the monochromator energy

has the effect of changing the source position, yc. Also,

changing the detector’s vertical position will alter the yd value.

Both have a direct impact on the calculated electron beam

position and angle, y and y0. Thus the system measures relative

values of position and angle and must be calibrated to obtain

absolute values.

The ability to determine the location of the beam centroid,

yd, and the K-edge, yc, are integral to the success of this

method. A fitting procedure will be used to determine the

location of each. To be properly fit there needs to be sufficient

intensity, detector resolution and vertical size to encompass

the profile along with any vertical motion that may occur. The

vertical beam size at the detector is a relatively weak function

of the energy selected by the monochromator. However, the

reflection chosen in the monochromator may have a strong

effect on the intensity since the reflection sets the mono-

chromator bandwidth.

In addition, the ability to determine yc will also depend on

the width of the K-edge and the thickness and density of the

contrast filter. A rough estimate of the optimal projected

iodine filter density was found to be �70 mg cm�2 by

numerical simulation. This estimate was based on a contrast to

noise model using Poisson statistics.

The width of the transmitted K-edge with the DCM will

depend on the intrinsic K-edge width for the contrast element

(�15 eV for iodine; Feiters et al., 2005). The K-edge will also

be blurred by the intrinsic energy width of the monochromator

[1.88 eV as discussed above for the Si (2,2,0) at 33.17 keV],

and will also be dispersed vertically, z, across the detector,

approximately as

dz

dE¼

tan �

ED; ð6Þ

where � is the Bragg angle, D is the source-to-detector

distance and E is the K-edge energy. For silicon (2,2,0) at the

iodine K-edge this spatial dispersion is 74 mm eV�1. There-

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J. Synchrotron Rad. (2015). 22, 946–955 Nazanin Samadi et al. � Phase-space beam position monitor 949

Figure 5Schematic showing the effects of the electron beam position and angledisplacements. The first column gives the position and angle, the secondcolumn is a schematic of the beam where the monochromator has beenremoved for clarity, the third and fourth columns show the beam and edgeprofile, respectively. The black line in each row represents the electronbeam position and angle zeros, the purple line shows the centroid of thebeam, the red dashed line shows the location of the same angle to themonochromator crystal or the edge location. (a, c) At y = 0. (a, b) At y0 =0. (b, d) At y > 0. (c, d) At y0 > 0.

fore, the 15 eV of energy spread will correspond to a spatial

width of 1.1 mm.

When compared with silicon (4,4,0) under similar condi-

tions the spatial dispersion at 33.17 keV will change to

150 mm eV�1 and the 15 eV energy spread will correspond to a

width of�2.2 mm which indicates increased spatial dispersion

sensitivity. But this sensitivity will come with a loss of intensity

of over a factor of six due to the decreased (4,4,0) bandwidth

(9.1 � 10�6) compared with the (2,2,0) bandwidth (56.6 �

10�6) and therefore, for the bulk of the measurements, we

chose silicon (2,2,0).

4. Implementation at BMIT

The experiments for this project were performed at the CLS

BMIT bend-magnet beamline 05B1-1. A silicon (2,2,0) and

(4,4,0) double-crystal monochromator was tuned to the iodine

K-edge at 33.17 keV. The vertical dispersion of the mono-

chromator allows an energy range that covers the K-edge of

iodine. Figs. 2(a)–2(c) show schematically how the system was

implemented in the beamline with a plan view at the top. In

this system the beam was split horizontally in two parts: one

side with a 60 mg cm�2 iodine filter and the other side with no

filter. A Hamamatsu flat-panel detector with 0.1 mm pixel size

was used to collect data. Measurements were made in the

POE-2 hutch, which was �25 m away from the source.

Two types of measurements were performed. One type was

made during the normal operational mode to assess the beam

stability. A second type was made during special shifts where

the synchrotron beam was intentionally moved at the source

location with specific vertical, horizontal and angular offsets.

This second type was used to assess, in part, the sensitivity of

the system and to independently measure the motions made to

the electron beam source in the ring.

Data were in the form of images of the split beam with the

iodine filter on one side and no filter on the other. Sets of 400

data images were saved into individual directories and a

measurement set might range from a few to several hundred

directories. It took around 12 s to collect 400 images for each

directory and roughly 1 min dead-time to save the data to the

disk. For each set of measurements, ten dark images (the

detector response without beam) and ten flat images (no

contrast agent in the beam) were also collected for data

normalization. These ten images were averaged to form single

‘dark’ and ‘flat’ images.

5. Data analysis method

To analyze the data, several procedures were written in IDL

(Interactive Data Language; ITT Visual Information Solu-

tions, Boulder, CO, USA). Regions for the unfiltered beam

side and the K-edge side were selected from the data and each

side was corrected for dark response. An example of the

regions chosen from the images is shown in Fig. 6.

The beam side data were used to determine yd which was

found by fitting the horizontally averaged vertical beam

profile using a Gaussian function. An example of this fitting

was shown in Fig. 1. The vertical direction at the detector, z,

was measured in terms of detector pixels that can be easily

converted into micrometers using the pixel size. The vertical

center of the detector was the origin used in this part of the

analysis.

The horizontally averaged K-edge side profile was

normalized by the matching region from the flat to form an I/I0

profile. However, the flat was corrected for vertical beam

motion by using the beam side of the data to vertically move

the flat prior to normalization. The low-intensity regions of

this corrected flat were ignored using a threshold value and

not used in the analysis. An example of this is shown in Fig. 7.

A number of fitting algorithms were used to find the loca-

tion of the K-edge in the filtered beam profile. In general,

three types of functions were investigated to fit the edge:

Gaussian, Lorentzian and Voigt. These functions were chosen

because they are mathematically simple and make physical

sense. The functions were used directly to fit the derivative of

the K-edge profile, and integrated versions of each were used

to fit the measured edge profile directly. Finally the K-edge

could be fit to the I/I0 values or the negative logarithm of the

I/I0 values. Of the 12 fit types the Gaussian fit to the derivative

of the negative logarithm of the profile was chosen due to its

simplicity and the robustness of the fit. For this analysis the

main parameter of interest in the fit was the transition center

location. Other parameters determined in the fit were the

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950 Nazanin Samadi et al. � Phase-space beam position monitor J. Synchrotron Rad. (2015). 22, 946–955

Figure 6Example data image. Regions are chosen from both image types for beamand edge analysis. The edge region is enhanced in the lower left corner tobetter show the K-edge whose location is indicated by the arrow.

Figure 7Summed normalized K-edge image across the sampling width; 100 pixelsin this case. The horizontal axis is in pixels and the origin is referenced tothe vertical middle of the detector.

amplitude, width and the background values. Fig. 8 shows a fit

to one of the data points.

6. Results and discussion

A number of measurements have been taken with the system.

In total, eight shifts (1 shift = 8 h) were used for the beam

motion measurements. These shifts were during normal

operations and by special request when the ring parameters

could be altered. During the special machine study shifts, the

electron beam was moved and measurements were made to

assess the response of the system.

6.1. System response to electron beam motions

The electron beam position and angle were varied in the

machine study shifts. To move the electron beam in the BMIT

sector, electron BPM (eBPM) target values were changed.

This change in target value moves the electron beam orbit

using dipole steering magnets. The eBPMs numbered 17 and

18 are located on the upstream and downstream sides of the

bend magnet which is our photon beam source (see Fig. 9).

The photon beam source is 5� into the 15� bend. Since we

observe the photon beam source point at an intermediate

location between the two eBPMs, there can be small differ-

ences in the electron beam vertical position and angle due to

the storage ring magnetic optics.

6.1.1. Electron beam vertical position measurements. For

vertical motion, the eBPM17 and eBPM18 target values were

changed by the same amount. The beam was moved vertically

between +100 and �100 mm in 0, �1, �2, �5, �10, �20 and

�100 mm increments. Examples are shown where the beam

is at the zero location (Fig. 10a), +100 mm (Fig. 10b) and

�100 mm (Fig. 10c). In those plots, 12 s of beam motion is

shown. It should be noted that the measured beam position

and angle are relative to the middle of the detector. Three data

lines are shown: red, which is the measured electron beam

position, y; blue, the electron beam angle multiplied by the

distance from the source to the detector,

Dy0 (this allows it to be plotted on the

same scale as the position); and purple,

the overall beam position, y + Dy0.

Trend plots of the electron beam

position and angle measurement as a

function of eBPM offset values are

shown in Figs. 11 and 12, respectively.

Some selected values are also given in

Table 1. The dashed horizontal line in

the figures identifies the measured

‘zero’ location where the electron beam

is at the zero location in eBPM units.

Clearly, there is good correlation

between the eBPM values and the beam

position and angle. The red line in

Fig. 11 and the blue line in Fig. 12 are

least-squares fits to the measured data.

For these data, 150 twelve-second

measurements (called a ‘slice’) were

made as the beam was moved. For each

beam location, between four and five

slices were taken. In reviewing Table 1,

the measured standard deviations are in

the 10 mm range for y, Dy0 and y + Dy0.

From Fig. 11, the vertical beam posi-

tion rate of change was determined to

be 1.807 � 0.02 mm per mm eBPM value

from the least-squares fit. From Fig. 12,

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J. Synchrotron Rad. (2015). 22, 946–955 Nazanin Samadi et al. � Phase-space beam position monitor 951

Figure 8Derivative of the negative logarithm of the profile shown in Fig. 7. TheGaussian fit parameters are shown in the upper right-hand corner. Forthis analysis only y0 or the peak center is used.

Figure 9Storage ring schematic and calculated electron beam trajectories. (a) Section of the storage ringaround the 05B1 magnet from which the measurements were made. The locations for eBPM17,eBPM18 and 5� source are indicated. The calculated trajectory for +100 mm vertical position foreBPM17 and eBPM18 are shown in (b) with the electron vertical position in red and angle in blue.(c) Trajectory for a +100 mm value at eBPM17 and �100 mm at eBPM18 which mostly creates anangle at the source location.

the vertical beam angle rate of change was similarly determine

to be 0.0301 � 0.0004 mrad per mm eBPM value. Based on

electron beam optics calculations for an ideal machine, the

predicted values should be 1.47 mm per mm eBPM value and

�0.034 mrad per mm eBPM value, respectively. The good

agreement between the experimentally determined and

calculated values is shown in the top row of Table 2.

6.1.2. Electron beam vertical angle measurements. Similar

measurements were made when the eBPM values were

changed asymmetrically to create electron beam angle at the

beamline. Tests were made with eBPM offsets between +20

and �20 mm in 0, �5, �10, �15 and �20 increments.

Plots of the electron beam position and angle as a function

of eBPM values are shown in Figs. 13 and 14, respectively.

Some selected values are also given in Table 3 and, as before,

the measured standard deviations are in the 10 mm range for

y, Dy0 and y + Dy0. The dashed horizontal line in the figures

identifies the measured zero location where the electron beam

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952 Nazanin Samadi et al. � Phase-space beam position monitor J. Synchrotron Rad. (2015). 22, 946–955

Figure 10Measurements of the beam vertical position, y, the effect of vertical angle,Dy0, and combined motion as a function of time for eBPM17/18 values of0 (a), +100 (b) and �100 (c). The vertical motions have been translatedinto millimeters using the 100 mm pixel size. The vertical zero is thevertical detector center.

Figure 11Electron vertical beam position in micrometers measured as the eBPM17and 18 are changed from �50 to +50 mm.

Figure 12Electron beam vertical angle in microradians measured as the eBPM17and 18 are changed from �50 to +50 mm. The measured angle inmicroradians is shown on the left axis and the vertical displacement thatangle creates at the detector position, Dy0, is shown on the right.

Table 1Selected measured electron vertical beam position, y, and angle, y0, as afunction of vertical electron beam motion defined by equal eBPM17 and18 values.

The slice number identifies the measurement. Columns showing the effect ofthe electron beam angle on beam position, Dy0, and the overall vertical beammotion, y + Dy0, at the detector, are given along with calculated standarddeviations. Each slice corresponds to 12 s of acquisition time.

Slice #BPM17/18 (mm) y (mm) y0 (mrad) Dy0 (mm) yþDy0 (mm)

2 0 �401 � 8 5.89 � 0.54 146 � 13 �255 � 1282 5 �385 � 8 6.01 � 0.56 150 � 14 �235 � 1295 10 �375 � 8 6.07 � 0.52 152 � 13 �223 � 1392 20 �356 � 8 6.34 � 0.53 158 � 13 �198 � 1299 30 �334 � 8 6.64 � 0.55 165 � 14 �168 � 13

105 40 �316 � 8 7.02 � 0.54 175 � 14 �141 � 13113 50 �297 � 8 7.34 � 0.53 190 � 13 �107 � 12121 �5 �396 � 8 5.45 � 0.51 136 � 13 �259 � 13125 �10 �406 � 8 5.34 � 0.52 133 � 13 �272 � 12133 �20 �430 � 8 5.24 � 0.55 131 � 14 �299 � 12139 �30 �448 � 8 4.97 � 0.53 124 � 13 �324 � 12146 �40 �461 � 8 4.52 � 0.52 113 � 13 �348 � 12153 �50 �467 � 8 4.16 � 0.53 103 � 13 �372 � 11

is at the zero location in eBPM units. The red line in Fig. 13

and the blue line in Fig. 14 are least-squares fits to the

measured data.

The measured and calculated beam responses are

summarized in the lower half of Table 2. Again, there is a good

agreement between the measured and ideal machine values.

6.2. Normal operations measurements

Measurements with the ps-BPM system were made during a

number of normal operation shifts between December 2013

and August 2014. During the December 2013 to early 2014

period the CLS storage ring was experiencing beam instabil-

ities from a storage ring dipole magnet power supply.

Fig. 15 shows 12 s measurements made during three

operational periods in December 2013, March 2014 and

August 2014. The top line is the

measured electron beam position, y, the

bottom line is the vertical displacement

due to angle, Dy0, and the middle line is

the sum of the two, y + Dy0. Each of the

three measurement periods are shown

side by side in the figure. The offsets for

the three position types have been

removed so that their average is zero to

make the comparison easier.

It is clear that the ring stability

improved dramatically during that time

period and that the instability measured arose primarily from

the angle displacements. Fig. 15 also shows measured standard

deviations of the positions, �y, �Dy0 and �yþDy0 . The standard

deviation of the electron beam position, �y, varied little over

the three periods. However, the standard deviation of the

vertical displacement due to angle, �Dy0 , dropped by a factor of

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J. Synchrotron Rad. (2015). 22, 946–955 Nazanin Samadi et al. � Phase-space beam position monitor 953

Table 2Measured and calculated detector response to vertical electron beam position and angle.

Vertical electron beam positions where eBPM17 and 18 are equal are shown in the upper two rows (upperrow: measured; lower row: calculated). Vertical beam angle where eBPM17 is equal to, but opposite signto, eBPM18 is shown in the bottom two rows. At the measurement location there is a mixture of positionand angle for both types of electron beam motion.

Position mm=mm offsetð Þ Angle mrad=mm offsetð Þ

Position motion(eBPM17 = eBMP18)

Measured 1.807 � 0.02 0.0301 � 0.0004Calculated 1.47 �0.034

Angle motion(eBPM17 = �eBPM18)

Measured �0.101 � 0.039 �0.842 � 0.005Calculated �0.06 �0.88

Figure 13Electron vertical beam position in micrometers measured as the eBPM17and �18 are changed from �20 to +20 mm.

Figure 14Electron beam vertical angle in microradians measured as the eBPM17and �18 are changed from �20 to +20 mm. The measured angle inmicroradians is shown on the left axis and the vertical displacement thatangle creates at the detector position, Dy0, is shown on the right.

Figure 15Beam phase-space measurements over a 12 s interval during normaloperations for three dates: December 2013, March 2014 and August 2014.The top line is the zero referenced electron beam position, y, the bottomline is the vertical displacement due to angle, Dy0, and the middle line isthe sum of the two, y + Dy0. Note the improvement in beam stability overthe nine-month period. The standard deviation values are shown aboveeach period.

Table 3Selected measured electron vertical beam position, y, and angle, y0, as afunction of electron beam angle defined by equal and opposite signeBPM17 and 18 values; the remainder of the table is for Dy0 and y + Dy0

as defined in Table 1 and in the text.

Slice #

BPM17/�18(mm) y (mm) y0 (mrad) Dy0 (mm) yþDy0 (mm)

9 5 �428 � 8 2.30 � 0.55 57 � 14 �371 � 1413 10 �430 � 8 �1.64 � 0.51 �41 � 13 �471 � 1320 20 �427 � 8 �9.63 � 0.51 �241 � 13 �667 � 1247 �5 �421 � 8 10.70 � 0.57 267 � 14 �154 � 1351 �10 �423 � 8 15.09 � 0.51 377 � 13 �46 � 1358 �20 �428 � 8 24.16 � 0.58 604 � 15 176 � 13

two in the same time. The standard deviation of the overall

beam displacement due to electron beam positon and angle,

�yþDy0 , is determined mostly by the electron beam angle.

The DCM could be responsible for some of the measured

beam motion due to vibrations and thermal motion. Internal

vibrations within the monochromator are somewhat mini-

mized as we used a gravity flow water system for cooling both

crystals in the DCM. Also the use of a copper and aluminium

filter dropped the incident power on the first crystal to below

2 W for the size of the beam and ring current used for the

experiments. Finally, based on our measurements, as the beam

is moved in the machine the error bar on the beam displace-

ment was typically less than 10 mm and the angle less than

0.5 mrad, indicating that the combination of the mono-

chromator and electron beam motions must be less than these

values.

7. Practical implementation of a ps-BPM

All of the proof-of-principle measurements required the use

of the entire beamline and as such would be completely

impractical as a monitor. Probably the most challenging aspect

of implementing such a monitor would be the dedicated use

of the DCM. The complexity of the DCM in which the two

crystals must be maintained in sub-microradian alignment in

the Bragg geometry could be mitigated by the use of a single-

crystal Laue or transmission-type monochromator. The Laue-

type monochromator is not so susceptible to crystal heating

effects as there is no thermal bump on the crystal’s surface.

Much of the power can be transmitted through where it can be

absorbed elsewhere. The width of the beam being used need

not be very wide as two line detectors can be used for the

beam and K-edge side measurements. A prototype Laue-type

system is being designed.

8. Conclusions

A unique method for simultaneously measuring the vertical

position and angle (phase space) of synchrotron photon beams

using the combination of X-ray diffraction and absorption

edges has been developed and tested at the BMIT beamline at

the Canadian Light Source. This system allows the measure-

ment of the photon beam centroid in phase space, and thus the

electron beam source position and angle, at a single location

along the beamline. Temporal stability and beam motion

system response measurements have been performed with

good results.

The sensitivity of this system is comparable with other

photon beam position monitors with detectable position

errors on the scale of 10 mm and angle errors of 0.5 mrad.

These errors are based on the noise level in a 12 s time

measurement with 400 time points.

We are optimistic that a compact dedicated system

employing a single transmission or Laue monochromator

coupled with a K-edge filter and two line detectors can be built

and implemented to make a practical device that uses a small

piece of the horizontal width of a bend-magnet or wiggler

white beam.

Such a phase-space system provides a more complete view

of beam motion in a synchrotron source and may be used to

improve the synchrotron source position and angle stability.

The ps-BPM also provides a better diagnostic should

instabilities or beam drift occur, and could be used to correct

experimental data for beam motion and to actively control the

trajectory of the photon beam in the beamline.

Acknowledgements

The authors acknowledge the financial support of Canadian

Institutes of Health Research (CIHR) Training Grant –

Training in Health Research Using Synchrotron Techniques

(NS, MM, BB), Saskatchewan Health Research Foundation

Team Grant (NS, DC), Natural Sciences and Engineering

Research Council of Canada (NSERC) Discovery Grant

(DC), the University of Saskatchewan (NS, MM), and Canada

Research Chair Program (DC). Research described in this

paper was performed at the Canadian Light Source, which is

funded by the Canada Foundation for Innovation, NSERC,

the National Research Council Canada, CIHR, the Govern-

ment of Saskatchewan, Western Economic Diversification

Canada, and the University of Saskatchewan.

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